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(Undeﬁned) l Grouping (UndeﬁneaD Games Questions 6-1 1 F u, Gunsel, Jackson, Kowalski, Lee, Mayer, and Ordoveza are
the only applicants being considered for some positions at a
nonproﬁt organization. Only applicants who are interviewed
will be hired. The hiring process must meet the following
constraints: If Gunsel is interviewed, Jackson is interviewed. If Jackson is interviewed, Lee is interviewed. F u is interviewed. F u is not hired, unless Kowalski is interviewed. Kowalski is not hired, unless Mayer is interviewed. If Mayer is hired, and Lee is interviewed, Ordoveza is
hired. 6. Which one of the following could be a complete and
accurate list of the applicants that are interviewed? (A) Fu, Gunsel (B) Fu, Jackson (C) Fu, Lee (D) Fu, Gunsel, Lee (E) Fu, Gunsel, Jackson 7. Which one of the following could be true? (A) Lee and Mayer are the only applicants
interviewed. (B) F u, Jackson, and Kowalski are the only applicants
interviewed. (C) Gunsel and one other applicant are the only
applicants interviewed. (D) Gunsel and two other applicants are the only
applicants interviewed. (E) Gunsel and three other applicants are the only
applicants interviewed. 8. If Mayer is not interviewed, which one of the following
must be true? (A) Kowalski is not interviewed. (B) Kowalski is interviewed but not hired. (C) Fu is not hired. (D) F u is hired but Kowalski is not hired. (E) F u is interviewed but Kowalski is not hired. 9. 10. 11. If Gunsel and ﬁve other applicants are the only applicants
interviewed, and if exactly three applicants are hired, then
which one of the following could be an accurate list of the
applicants hired? (A) Fu, Lee, Mayer (B) Fu, Kowalski, Mayer (C) Kowalski, Lee, Ordoveza
(D) Gunsel, Jackson, Mayer
(E) Gunsel, Jackson, Lee If every applicant that is interviewed is hired, and if Lee is
hired, then each of the following applicants must be
interviewed EXCEPT: (A) F u (B) Jackson
(C) Kowalski
(D) Mayer
(E) Ordoveza If Ordoveza is not interviewed, and if exactly four
applicants are hired, then which one of the following must
be false? (A) Lee is hired. (B) Mayer is hired. (C) Jackson is interviewed.
(D) Kowalski is interviewed.
(E) Gunsel is interviewed.1 1 PT 23, Game 2 Grouping (UndeﬁneaD Games I Questions 7-13 A music store carries ten types of CDsiboth new and used of
each of jazz, opera, pop, rap, and soul. The store is having a
sale on some of these types of CDs. The following conditions
must apply: Used pop is on sale; new opera is not. If both types of pop are on sale, then all soul is. If both types of jazz are on sale, then no rap is. If neither type of jazz is on sale, then new pop is. If either type of rap is on sale, then no soul is. 7. Which one of the following could be a complete and
accurate list of the types of CDs that are on sale? (A) new jazz, used jazz, used opera, used pop, new
rap (B) new jazz, used pop, used rap, new soul (C) used opera, used pop, new rap, used rap (D) used opera, new pop, used pop, new soul (E) used jazz, used pop, new soul, used soul 8. If new soul is not on sale, then which one of the following
must be true? (A) New rap is not on sale. (B) New rap is on sale. (C) Used opera is not on sale. (D) At least one type of jazz is not on sale.
(B) At least one type of pop is not on sale. 9. If both types of jazz are on sale, then which one of the
following is the minimum number of types of new CDs
that could be included in the sale? (A) one
(B) two
(C) three
(D) four
(E) ﬁve 10. Which one of the following CANNOT be true? 11. 12. 13. (A) Neither type of opera and neither type of rap is on
sale. (B) Neither type of jazz and neither type of opera is
on sale. (C) Neither type of opera and neither type of soul is
on sale. (D) Neither type of jazz and neither type of soul is on
sale. (E) Neither type of jazz and neither type of rap is on
sale. If neither type of jazz is on sale, then each of the
following must be true EXCEPT: (A) Used opera is on sale.
(B) New rap is not on sale.
(C) Used rap is not on sale.
(D) New soul is on sale.
(E) Used soul is on sale. If new soul is the only type of new CD on sale, then
which one of the following CANNOT be true? (A) Used jazz is not on sale.
(B) Use opera is not on sale.
(C) Used rap is not on sale.
(D) Used soul is on sale. (E) Used soul is not on sale. If exactly four of the ﬁve types of used CDs are the only
CDs on sale, then which one of the following could be
true? (A) Used jazz is not on sale. (B) Used opera is not on sale. (C) Used rap is not on sale. (D) Neither type of jazz is on sale. (E) Neither type of rap and neither type of soul is on
sale. 2PT31,Game2 Grouping (UndeﬁneaD Games Questions 6-12 Bird-watchers explore a forest to see which of the following
six kinds of birdsigrosbeak, harrier, jay, martin, shrike,
wreniit contains. The ﬁndings are consistent with the
following conditions: If harriers are in the forest, then grosbeaks are not. If jays, martins, or both are in the forest, then so are
harriers. If wrens are in the forest, then so are grosbeaks. If jays are not in the forest, then shrikes are. 6. Which one of the following could be a complete and 8. accurate list of the birds NOT in the forest? (A) jays, shrikes (B) harriers, grosbeaks (C) grosbeaks, jays, martins (D) grosbeaks, martins, shrikes, wrens
(E) martins, shrikes If both martins and harriers are in the forest, then which
one of the following must be true? (A) Shrikes are the only other birds in the forest. (B) Jays are the only other birds in the forest. (C) The forest contains neither jays nor shrikes. (D) There are at least two other kinds of birds in the
forest. (E) There are at most two other kinds of birds in the
forest. If jays are not in the forest, then which one of the
following must be false? (A) Martins are in the forest. (B) Harriers are in the forest. (C) Neither martins nor harriers are in the forest. (D) Neither martins nor shrikes are in the forest. (E) Harriers and shrikes are the only birds in the
forest. 9. 10. ll. 12. Which one of the following is the maximum number of
the six kinds of birds the forest could contain? (A) two
(B) three
(C) four
(D) ﬁve
(E) six Which one of the following pairs of birds CANNOT be
among those birds contained in the forest? (A) jays, wrens (B) jays, shrikes
(C) shrikes, wrens
(D) jays, martins
(E) shrikes, martins If grosbeaks are in the forest, then which one of the
following must be true? (A) Shrikes are in the forest. (B) Wrens are in the forest. (C) The forest contains both wrens and shrikes.
(D) At most two kinds of birds are in the forest.
(B) At least three kinds of birds are in the forest. Suppose the condition is added that if shrikes are in the
forest, then harriers are not. If all other conditions remain
in effect, then which one of the following could be true? (A) The forest contains both jays and shrikes. (B) The forest contains both wrens and shrikes. (C) The forest contains both martins and shrikes. (D) Jays are not in the forest, whereas martins are. (E) Only two of the six kinds of birds are not in the
forest.3 3 PT 33, Game 2 Grouping (UndeﬁneaD Games I Questions 1-6 A ﬁ'uit stand carries at least one kind of the following kinds of
fruit: ﬁgs, kiwis, oranges, pears, tangerines, and watermelons.
The stand does not carry any other kind of fruit. The selection
of fruits the stand carries is consistent with the following
conditions:
If the stand carries kiwis, then it does not carry pears.
If the stand does not carry tangerines, then it carries kiwis.
If the stand carries oranges, then it carries both pears and
watermelons.
If the stand carries watermelons, then it carries ﬁgs or
tangerines or both. 1. Which one of the following could be a complete and
accurate list of the kinds of ﬁ'uit the stand carries? (A) oranges, pears (B) pears, tangerines (C) oranges, pears, watermelons (D) oranges, tangerines, watermelons
(E) kiwis, oranges, pears, watermelons 2. Which one of the following could be the only kind of ﬁ'uit
the stand carries? (A) ﬁgs (B) oranges (C) pears (D) tangerines
(E) watermelons 3. Which one of the following CANNOT be a complete and
accurate list of the kinds of ﬁ'uit the stand carries? (A) kiwis, tangerines (B) tangerines, watermelons (C) ﬁgs, kiwis, watermelons (D) oranges, pears, tangerines, watermelons
(E) ﬁgs, kiwis, oranges, pears, watermelons 4. If the stand carries no watermelons, then which one of the following must be true? (A) The stand carries kiwis. (B) The stand carries at least two kinds of ﬁ'uit
(C) The stand carries at most three kinds of ﬁ'uit.
(D) The stand carries neither oranges nor pears.
(E) The stand carries neither oranges nor kiwis. If the stand carries watermelons, then which one of the
following must be false? (A) The stand does not carry ﬁgs. (B) The stand does not carry tangerines. (C) The stand does not carry pears. (D) The stand carries pears but not oranges.
(E) The stand carries pears but not tangerines. If the condition that if the fruit stand does not carry
tangerines then it does carry kiwis is suspended, and all
other conditions remain in effect, then which one of the
following CANNOT be a complete and accurate list of the
kinds of fruit the stand carries? (A) pears (B) ﬁgs, pears (C) oranges, pears, watermelons (D) ﬁgs, pears, watermelons (E) ﬁgs, oranges, pears, watermelons4 4 PT 36, Game 1 pg. 1
6. 7.
8.
9.
10.
11. PT 23, Game 2 UUUﬁD'JD'JD'JO GROUPING (UNDEFINED) GAMES PT 31, Game 2 PT 33, Game 2 PT 36, Game 1 pg-2 pg-3 pg-4
7. E 6. D 1. B
8. E 7. E 2. D
9. A 8. D 3. E
10. D 9. C 4. C
11. A 10. A 5. E
12. A 11. A 6. C
13. C 12. B ...
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